Saved in:
Bibliographic Details
Main Authors: Wei, Yashi, Hu, Jiang, Bai, Zhidong
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2511.01603
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • A large class of statistics can be formulated as smooth functions of sample means of random vectors. In this paper, we propose a general partial Cramér's condition (GPCC) and apply it to establish the validity of the Edgeworth expansion for the distribution function of these functions of sample means. Additionally, we apply the proposed theorems to several specific statistics. In particular, by verifying the GPCC, we demonstrate for the first time the validity of the formal Edgeworth expansion of Pearson's correlation coefficient between random variables with absolutely continuous and discrete components. Furthermore, we conduct a series of simulation studies that show the Edgeworth expansion has higher accuracy.